SEATTLE (Reuters) - A Hispanic advocacy group urged the U.S. Justice Department on Tuesday to conduct its own investigation into the fatal police shooting in Washington state of an unarmed Mexican immigrant who ran from officers after throwing rocks at them.

Consejo Latino Chairman Felix Vargas complained of an inherent conflict of interest in having local authorities investigate the Feb. 10 slaying of Antonio Zambrano-Montes in Pasco, a small city in an agricultural hub with a large Hispanic community and a largely white power structure.

"It appears inescapable that the lethal force applied by these police officers was excessive in the extreme and, as such, it constituted a violation of Mr. Zambrano's constitutional rights," Vargas wrote in a letter to the Justice Department.

"Any investigation of this killing conducted by fellow police officers will have no credibility whatsoever," he added.

Vargas noted that police officers have been cleared of any wrongdoing in three shootings over the past six months.

His organization's call for a separate federal inquiry follows similar demands in the wake of the police killings of two unarmed black men last year by white police officers in Ferguson, Missouri, and in New York City.

Several hundred people protested on Saturday over the killing in Pasco, some 200 miles (320 km) southeast of Seattle. On Friday, the Mexican government condemned the killing as a disproportionate use of lethal force.

Franklin County coroner Dan Blasdel has ordered a seven-member jury to decide whether the killing was justified, after which a prosecutor will decide whether to pursue charges, he said.

The Justice Department did not respond to requests for comment. An FBI spokeswoman in Seattle said the agency was monitoring the local investigation.

Pasco Police Captain Ken Roske said the department is not involved in the investigation and welcomed an independent inquiry.

Pasco police said Zambrano-Montes, an orchard worker from Mexico's Michoacan state, was not armed during the incident, which began in a grocery store parking lot, but noted that he pelted three officers with rocks and ignored commands to stop. The officers involved have been placed on administrative leave.

In a video filmed by a motorist and posted online, Zambrano-Montes is seen running from officers before they fire multiple times.

Vargas described Zambrano-Montes as a "troubled young man" who has used crystal meth and, a few months back, was briefly arrested in an incident in which he was shot with a stun gun.